Evaluate 512^(2/3)

Problem

512^(2/3)

Solution

1. Rewrite the expression using the properties of rational exponents, where a^(m/n)=(√(n,a))^m

512^(2/3)=(√(3,512))^2

2. Evaluate the cube root of 512 by identifying that 8×8×8=512

√(3,512)=8

3. Substitute the result back into the expression and square the value.

8^2=64

Final Answer

512^(2/3)=64

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